[r-t] Synergy of two threads: New Grandsire meets method extension

[Don Morrison]

All this discussion of New Grandsire, combined with a recent rereading
of the Decision on method extension, has me wondering about an obscure
point.

C. 1. (a) says "In this Part it is assumed that the method is started
from a change such that the treble is the hunt bell or a principal
hunt."

Imagine a method with N principal hunts. There are typically N
distinct rotations that meet the above criterion. Let's call them R1,
R2, ... RN.

Is a legal extension of, say, R2, guaranteed to be a rotation of a
legal extension of R1? Any proofs or counterexamples?

Because of various symmetries there might be fewer than N distinct
rotations, or rather multiple rotations might result in exactly the
same thing. Or if the principle hunts are sufficiently bizarre there
might be more possible rotations. Does this affect the
answer to the preceding question?



-- 
Don Morrison <dfm at ringing.org>
"When my son was eight months old, it could truthfully be said that he
devoured literature....He was, of course, not the first child to indulge
in bibliophagy. The great Philadelphia bookdealer A.S.W. Rosenbach deduced
that one reason first editions of _Alice in Wonderland_ were so scarce
was that so many of them had been eaten."     -- Anne Fadiman, _Ex Libris_